A key aim is to provide an insight into the interactions between these areas, in particular to modern applications such as coding and cryptography.
If taken as part of a BSc degree, courses which must be passed before this courses may be attempted:
- MT2116 Abstract mathematics.
This full course develops the mathematical methods of discrete mathematics and algebra and will emphasis their applications.
- Counting: selections, inclusion-exclusion, partitions and permutations, Stirling numbers, generating functions, recurrence relations.
- Graph Theory: basic concepts (graph, adjacency matrix, etc.), walks and cycles, trees and forests, colourings.
- Set Systems: matching, finite geometries, block designs.
- Abstract groups: revision of key concepts such as cyclic groups, subgroups, homomorphisms and Lagrange’s theorem. Conjugation and normal subgroups. Group actions.
- Applications of algebra to discrete mathematics I: permutations, orbits and stabilisers, the orbit-stabiliser theorem; applications to counting problems.
- Rings and polynomials: the Euclidean algorithm for polynomials, integral domains, ideals, factor rings, fields, field extensions.
- Finite fields: construction, the primitive element theorem, and finite linear algebra.
- Applications of algebra to discrete mathematics II: finite Geometry: designs, affine and projective planes.
- Error-correcting codes: linear codes, cyclic codes, perfect codes.
If you complete the course successfully, you should be able to:
- Demonstrate knowledge definitions, concepts and methods in the topics covered and how to apply these
- Find and formulate simple proofs
- Model situations in a mathematical way and derive useful results.
Unseen written exam (3 hrs).
- Biggs, N. Discrete mathematics. Oxford: Oxford University Press, 2002.
- Cameron, P.J. Introduction to Algebra. Oxford: Oxford University Press, 2008.
- Cameron, P.J. Combinatorics. Oxford: Oxford University Press, 2008.
Course information sheets
Download the course information sheets from the LSE website.